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Journals / International Journal of Engineering and Applied Sciences / 2026 / Volume: 10 Issue: 2

Derivation of Nonlocal Finite Element Formulation for Nano Beams

Ömer Civalek
Hayri Metin Numanoglu
Büşra Uzun
Pages
—
Publication Date
2018-08-15
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Size-dependent stiffness and mass matrix are derived for Euler-Bernoulli beams.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present paper, a new nonlocal formulation for vibration derived for nano beam lying on elastic matrix.
📊
Key Findings & Data:The formulation is based on the cubic shape polynomial functions via finite element method.
💡
Conclusion & Impact:Size-dependent stiffness and mass matrix are derived for Euler-Bernoulli beams.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Size-depended vibration · cubic shape functions · Nonlocal elasticity

Abstract

In the present paper, a new nonlocal formulation for vibration derived for nano beam lying on elastic matrix. The formulation is based on the cubic shape polynomial functions via finite element method. The size effect on finite element matrix is investigated using nonlocal elasticity theory. Finite element formulations and matrix coefficients have been obtained for nano beams. Size-dependent stiffness and mass matrix are derived for Euler-Bernoulli beams.

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Cite This Article

Civalek, Ö., Numanoglu, H. M., Uzun, B. (2018). Derivation of Nonlocal Finite Element Formulation for Nano Beams. International Journal of Engineering and Applied Sciences, Volume: 10 Issue: 2. https://doi.org/10.24107/ijeas.450239

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